So, it's possible for them to hold the NICS check without holding the person data. NICS is identified by a transaction ID and, at least as I understood it (NICS is an FBI system, so we had limited insight from the ATF, and as a contractor, I had possibly less insight than an ATF agent proper), the PII (Personally Identifiable Information) is purged from the NICS check upon completion of the check.

There might be, and probably is (at least) a record of the transactions that were processed and the result of the transaction. Also, as I understand it, if the check fails (hence, no gun is disbursed), then the PII may be held longer to aid potential investigations.

From the ATF's perspective though, PII definitely isn't kept, or at least wasn't as of 6 years ago. I honestly don't remember the specs on failed checks. I don't think that it did, but that isn't to say that if they are prepping for an investigation of an FFL that they couldn't requery the FBI for more thorough NICS records than what they hold in their own systems.